Manufacture of high-density, alumina (Al.sub.2 O.sub.3)-based polycrystalline sintered ceramics abrasive grains by a sol-gel method is known. Japanese Patent Publication JP-A-56-32369 discloses gelation of alumina monohydrate together with a precursor or precursors of at least one reforming component followed by dehydration and drying as well as sintering. The reforming component used in this case includes oxides of Co, Hf, Mg, Ni, Zn, and Zr. Japanese Patent Publication JP-A-60-231462 describes a method for the manufacture of alumina sol/gel in which increase of density of alumina is promoted by the addition of .alpha.-alumina seed crystals, and also that a crystal growth control agent comprising oxides of Si, Cr, Mg, and Zr.may be added to the gel. In particular, Japanese Patent Publication JP-A-61-254685 describes a method of adding .alpha.-alumina, .alpha.-ferric oxide or their precursors as a nucleating agent into a sol, and that the gel may contain precursors of oxides of Mg, Zn, Co, Ni, Zr, Hf, Cr and Ti.
The alumina-based sintered abrasive grains produced by the sol-gel method disclosed in the above-described Japanese Patent Publication JP-A-60-231462 make use of .alpha.-aluminization of alumina-based dry gel, and further of reduction in transformation energy of .alpha.-aluminization caused by the addition of fine grains of .alpha.-alumina to an alumina sol. Sintering the dry gel at a temperature no higher than 1,400.degree. C gives rise to a ceramics material composed of crystals of a fine structure having a particle diameter of from 0.2 to 0.4 .mu.m and a density of no lower than 90% of the theoretical density. When the material is used as an abrasive grain, it shows grindability superior to that of a monocrystalline abrasive grain obtained by a conventional fusion method. This is considered to be ascribable to the fine crystalline structure of a particle diameter of from 0.2 to 0.4 .mu.m.
However, ceramics materials having a fine crystalline structure of a particle diameter of no greater than 0.2 .mu.m, a density of no lower than 90% of the theoretical density and a hardness of no lower than 16 GPa cannot be obtained by the method disclosed in Japanese Patent Publication JP-A-60-231462.